# KAOPEN Deep Probe: Is the Openness Finding Recoverable?

The original KAOPEN interaction was significant in the extensions/net-gross papers.
Phase 7 Test 5 showed it null. This probe tests whether any specification recovers it.

**KAOPEN ceiling bunching**: 1713/7156 (23.9%) at maximum value.
OECD at ceiling: 53.7%. Correlation with income: 0.50, with OECD: 0.40.

## Results

| DV | Test | Z₁×Openness | p-value | N | Countries |
|---|---|---|---|---|---|
| ca_gdp | T0: Full KAOPEN | 10.087 | 0.1393 | 6780 | 178 |
| ca_gdp | T1: Ceiling excluded | -14.362 | 0.1068 | 5107 | 168 |
| ca_gdp | T2a: OECD only | -0.803 | 0.9479 | 1503 | 37 |
| ca_gdp | T2b: Non-OECD only | 6.822 | 0.4246 | 5277 | 141 |
| ca_gdp | T3: Trade openness | 42.510*** | 0.0012 | 6506 | 176 |
| ca_gdp | T4: Residualized KAOPEN | -1.809 | 0.8170 | 6780 | 178 |
| ca_gdp | T5: KA+Income horse race | -4.165 | 0.5818 | 6780 | 178 |
| ca_gdp | T6: Non-OECD below ceiling | -18.537* | 0.0672 | 4411 | 136 |
| ca_gdp | T7: High-income KAOPEN | 20.322 | 0.1207 | 2202 | 58 |
| gross_savings_gdp | T0: Full KAOPEN | -11.521 | 0.1835 | 5885 | 164 |
| gross_savings_gdp | T1: Ceiling excluded | -8.526 | 0.4469 | 4364 | 154 |
| gross_savings_gdp | T2a: OECD only | 8.782 | 0.3892 | 1489 | 37 |
| gross_savings_gdp | T2b: Non-OECD only | -9.917 | 0.3662 | 4396 | 127 |
| gross_savings_gdp | T3: Trade openness | 105.324*** | 0.0000 | 6577 | 175 |
| gross_savings_gdp | T4: Residualized KAOPEN | -11.113 | 0.2493 | 5885 | 164 |
| gross_savings_gdp | T5: KA+Income horse race | -11.973 | 0.2130 | 5885 | 164 |
| gross_savings_gdp | T6: Non-OECD below ceiling | -7.044 | 0.5914 | 3682 | 122 |
| gross_savings_gdp | T7: High-income KAOPEN | -11.284 | 0.3466 | 2091 | 54 |
| gross_investment_gdp | T0: Full KAOPEN | -3.540 | 0.5558 | 5857 | 163 |
| gross_investment_gdp | T1: Ceiling excluded | -1.079 | 0.8972 | 4328 | 152 |
| gross_investment_gdp | T2a: OECD only | -21.173* | 0.0593 | 1489 | 37 |
| gross_investment_gdp | T2b: Non-OECD only | -0.707 | 0.9259 | 4368 | 126 |
| gross_investment_gdp | T3: Trade openness | -23.532*** | 0.0032 | 6538 | 174 |
| gross_investment_gdp | T4: Residualized KAOPEN | -2.777 | 0.6852 | 5857 | 163 |
| gross_investment_gdp | T5: KA+Income horse race | -2.095 | 0.7587 | 5857 | 163 |
| gross_investment_gdp | T6: Non-OECD below ceiling | 5.457 | 0.5726 | 3646 | 120 |
| gross_investment_gdp | T7: High-income KAOPEN | -8.966 | 0.2486 | 2115 | 55 |

## Verdict

- Tests run: 27
- Significant at 5%: 3
- Marginal (5-10%): 2
- Null: 22

**Conclusion**: KAOPEN (de jure financial openness) is null in 24/27 specifications.
The 3 significant results are all **trade openness** (T3), a different measure entirely.
Residualized KAOPEN (T4) is null everywhere. The horse race (T5) kills KAOPEN while
income survives. The original KAOPEN finding was a proxy for income group: high-income
countries have both open capital accounts AND stronger demographic-CA effects, but
openness itself does not moderate the relationship.

**Trade openness** (de facto) does show genuine moderation: +42.5*** on CA, +105.3***
on savings, -23.5*** on investment. This is consistent with trade integration amplifying
the savings channel and suppressing investment (factor price equalization). But this
is a different finding from the original KAOPEN claim and requires separate investigation
to rule out small-country size confounds (trade/GDP correlates with country size).
